NCERT Solutions Class 6th Maths Chapter – 7 Fractions Exercise – 7.3

Question 1. Write the fractions. Are all these fractions equivalent?

Solution-

(a) (i) Shaded Part = 1/2
(ii) Shaded Part = 2/4 = 2 ÷ 2/4 ÷ 2 = 1/2
(iii) Shaded Part 3/6 = 3 ÷ 3/6 ÷ 3 = 1/2
(iv) Shaded Part 4/8 = 4 ÷ 4/8 ÷ 4 = 1/2

∴ All fractions are equivalent

(b) (i) Shaded Part = 4/12 = 4 ÷ 4/12 ÷ 3 = 1/3
(ii) Shaded Part = 3/9 = 3 ÷ 3/9 ÷ 3 =1/3
(iii) Shaded Part = 2/6 = 2 ÷ 2/6 ÷ 2 = 1/3
(iv) Shaded Part = 1/3
(v) Shaded Part = 6/15 = 6 ÷ 3/15 ÷ 3 = 2/5

Since all the fractions in their simplest form are not equal.
∴ They are not equivalent fractions.

Question 2. Write the fractions and pair up the equivalent fractions from each row.

Solution – 

(a) 1/2
(b) 4/6 = 4 ÷ 2/6 ÷ 2 = 2/3
(c) 3/9 = 3 ÷ 3/9 ÷ 3 = 1/3
(d) 2/8 = 2 ÷ 2/8 ÷ 2 = 1/4
(e) 3/4

(i) 6/18 = 6 ÷ 6/18 ÷ 6 = 1/3
(ii) 4/8 = 4 ÷ 4/8 ÷ 4 = 1/2
(iii) 12/16 = 12 ÷ 4/16 ÷ 4 = 3/4
(iv) 8/12 = 8 ÷ 4/12 ÷ 4 = 2/3
(v) 4/16 = 4 ÷ 4/16 ÷ 4 = 1/4

The following pairs of fractions- represent the equivalent fractions.
(a) and (ii) = 1/2
(b) and (iv) = 2/3
(c) and (i) = 1/3
(d) and (v) = 1/4
(e) and (iii) = 3/4

Question 3. Replace ▢ in each of the following by the correct number-

(a) 2/7 = 8/▢
(b) 5/8 = 10/▢
(c) 3/5 = ▢/20
(d) 45/60 = 15/▢
(e) 18/24 = ▢/4

Solution –

Question 4. Find the equivalent fraction of 3/5 having-

(a) Denominator 20
(b) Numerator 9
(c) Denominator 30
(d) Numerator 27

Solution –

(a) Here, we require denominator 20.
Let N be the numerator of the fractions
∴ N/20 = 3/5 ⇒ 5 × N = 20 × 3
⇒ N = 20 × 3/5 = 12
∴ The required fraction is 12/20

(b) Here, we required numerator 9.
Let D be the denominator of the fraction.
∴ 9/D = 3/5 ⇒ 3 × D = 9 × 5
⇒ D = 9 × 5/3 = 15
∴ The required fraction is 9/15.

(c) Here, we required denominator 30.
Let N be the numerator of the fraction.
∴ N/30 = 3/5 ⇒ 5 × N = 3 × 30
⇒ N = 3 × 30/5 = 18
∴ The required fraction is 18/30.

(d) Here, we required numerator 27.
Let D be the denominator of the fraction.
∴ 27 = 3/5 ⇒ 3 × D = 5 × 27
⇒ D = 5 × 27/3 = 45
∴ The required fraction is 27/45.

Question 5. Find the equivalent fraction of 3648 with-

(a) Numerator 9
(b) Denominator 4

Solution –

(a) Given that numerator = 9
∴ 9/D= 36/48 ⇒ D × 36 = 9 × 48
⇒ D = 9 × 48/36 = 12
So, the equivalent fraction is 9/12.

(b) Given that denominator = 4
∴ N\4 = 3648 ⇒ N x 48 = 4 x 36
⇒ N = 4 x 3648 = 3
So, the equivalent fraction is 3/4 .

Question 6. Check whether the given fractions are equivalent-

(a) 5/9, 30/54
(b) 3/10, 12/50
(c) 7/13, 5/11

Solution –

(a) 5/9 and 30/54
We have 5 x 54 = 270
and 9 x 30 = 270
Here 5 x 54 = 9 x 30
∴ 5/9 and 30/54 are equivalent fractions.

(b) 3/10 and 12/50
We have 3 x 50 = 150
and 10 x 12 = 120
Here 3 x 50 ≠ 10 x 12
∴ 3/10 and 12/50 are not equivalent fractions.

(c) 7/13 and 5/11
We have 7 x 11 = 77 and 5 x 13 = 65
Here 7 x 11 ≠ 5 x 13
∴ 7/13 and 5/11 are not equivalent fractions.

Question 7. Reduce the following fractions to simplest form-

(a) 48/60
(b) 150/60
(c) 84/98
(d) 12/52
(e) 7/28

Solution –

Question 8. Ramesh had 28 pencils, Sheelu had 50 pencils and Jamaal had 80 pencils. After 4 months, Ramesh used up 10 pencils, Sheelu used up 25 pencils and Jamaal used up 40 pencils. What fraction did each use up? Check if each has used up an equal fraction of her/his pencils.

Solution –

Ramesh used up 10 pencils out of 20 pencils.
∴ Fraction = 10/20 = 1/2

Sheelu used up 25 pencils out of 50 pencils.
∴ Fraction = 25/50 = 25 ÷ 25/50 ÷ 25 = 1/2

Jamaal used up 40 pencils out of 80 pencils.
∴ Fraction = 40/80 = 4/8 = 1/2

Yes, each has used up an equal fractions, i.e., 12.

Question 9. Match the equivalent fractions and write two more for each.

Solution –

(i) 250/400
GCF of 250 and 400 is 50. Dividing the numerator and denominator by GCF, we get
250/400 ÷ 50/50 = 5/8
∴ (i) ⇔ (d)
Two more equivalent fractions are 5/8 × 2/2 = 10/16 and 5/8 × 3/3 = 15/24.

(ii) 180/200
GCF of 180 and 200 is 20. Dividing the numerator and denominator by GCF, we get
180/200 ÷ 20/20 = 9/10
∴ (ii) ⇔ (e).
Two more equivalent fractions are 9/10 × 2/2 = 18/20 and 9/10 × 3/3 = 27/30.

(iii) 660/990
GCF of 660 and 990 is 330. Dividing the numerator and denominator by GCF, we get
660/990 ÷ 330/330 = 2/3
∴ (iii) ⇔ (a).
Two more equivalent fractions are 2/3 × 2/2 = 4/6 and 2/3 × 3/3 = 6/9.

(iv) 180/360
GCF of 180 and 360 is 18. Dividing the numerator and denominator by GCF, we get
180/360 ÷ 18/18 = 1/2.
∴ (iv) ⇔ (c).
Two more equivalent fractions are 1/2 × 2/2 = 2/4 and 1/2 × 3/3 = 3/6.

(v) 220/550
GCF of 220 and 550 is 110. Dividing the numerator and denominator by GCF, we get
220/550 ÷ 110/110 = 2/5.
∴ (v) ⇔ (b).
Two more equivalent fractions are 2/5 × 2/2 = 4/10 and 2/5 × 3/3 = 6/15.